Package {wdm}

Weighted Dependence Measures

Description

Provides efficient implementations of weighted dependence measures and related asymptotic tests for independence. Implemented measures are the Pearson correlation, Spearman's rho, Kendall's tau, Blomqvist's beta, Hoeffding's D, and Chatterjee's xi; see, e.g., Nelsen (2006) <doi:10.1007/0-387-28678-0>, Hollander et al. (2015, ISBN:9780470387375), and Chatterjee (2021) <doi:10.1080/01621459.2020.1758115>.

Author(s)

Maintainer: Thomas Nagler mail@tnagler.com

Authors:

• Thomas Nagler mail@tnagler.com

See Also

Useful links:

• https://tnagler.github.io/wdm-r/

• https://github.com/tnagler/wdm-r

• Report bugs at https://github.com/tnagler/wdm-r/issues

Independence Tests for Weighted Dependence Measures

Description

Computes a dependence measure and its asymptotic independence test for two numeric vectors.

Usage

indep_test(
  x,
  y,
  method = "pearson",
  weights = NULL,
  remove_missing = TRUE,
  alternative = "two-sided",
  seeds = NULL,
  y_continuous = TRUE
)

Arguments

Details

Available methods:

• "pearson": Pearson correlation

• "spearman": Spearman's \rho

• "kendall": Kendall's \tau

• "blomqvist": Blomqvist's \beta

• "hoeffding": Hoeffding's D

• "chatterjee": Chatterjee's \xi

Partial matching of method names is enabled. This implementation of Hoeffding's D does not support tied observations; test results are invalid when ties are present. It supports only the two-sided alternative. The natural one-sided alternative for Chatterjee's \xi is "greater".

Chatterjee's \xi measures the dependence of y on x. Analytic inference with unequal weights requires a continuous response and assumes that weights are fixed or depend only on x. It is unavailable when the response is discrete or tied and weights are unequal.

Value

A one-row data frame containing the estimate, transformed test statistic, p-value, effective sample size, method, and alternative.

Examples

x <- rnorm(100)
y <- rpois(100, 1)
w <- runif(100)

indep_test(x, y, method = "kendall")               # unweighted
indep_test(x, y, method = "kendall", weights = w)  # weighted

Computing weighted ranks

Description

For observations without ties, the weighted rank of X_i among X_1, \dots, X_n with weights w_1, \dots, w_n is

\frac{n}{\sum_{k = 1}^n w_k} \sum_{j = 1}^n w_j 1[X_j \le X_i].

Thus, multiplying every weight by the same positive constant does not change the ranks, and unit weights reproduce ordinary ranks. Tied values are handled according to ties_method.

Usage

rank_wtd(x, weights = numeric(), ties_method = "average")

Arguments

Value

a vector of ranks.

Examples

x <- rnorm(100)
w <- rexp(100)
rank(x)
rank_wtd(x, w)

Weighted Dependence Measures

Description

Computes a (possibly weighted) dependence measure between x and y if these are vectors. If either argument is a matrix, the measures between all corresponding columns are computed.

Usage

wdm(
  x,
  y = NULL,
  method = "pearson",
  weights = NULL,
  remove_missing = TRUE,
  seeds = NULL
)

Arguments

Details

Available methods:

• "pearson": Pearson correlation

• "spearman": Spearman's \rho

• "kendall": Kendall's \tau

• "blomqvist": Blomqvist's \beta

• "hoeffding": Hoeffding's D

• "chatterjee": Chatterjee's \xi Partial matching of method names is enabled.

Spearman's \rho and Kendall's \tau are corrected for ties if there are any. This implementation of Hoeffding's D does not support tied observations; estimates are invalid when ties are present. Chatterjee's \xi measures the dependence of y on x and is generally asymmetric. Consequently, wdm(x, method = "chatterjee") need not return a symmetric matrix.

Value

A numeric scalar when both inputs are vectors or one-column objects; otherwise, a matrix containing the dependence measure for every pair of columns.

Examples

##  dependence between two vectors
x <- rnorm(100)
y <- rpois(100, 1)
w <- runif(100)
wdm(x, y, method = "kendall")               # unweighted
wdm(x, y, method = "kendall", weights = w)  # weighted

##  dependence in a matrix
x <- matrix(rnorm(100 * 3), 100, 3)
wdm(x, method = "spearman")               # unweighted
wdm(x, method = "spearman", weights = w)  # weighted

##  dependence between columns of two matrices
y <- matrix(rnorm(100 * 2), 100, 2)
wdm(x, y, method = "hoeffding")               # unweighted
wdm(x, y, method = "hoeffding", weights = w)  # weighted